A control system is a dynamical system that affects the behaviour of another system. Examples of control systems can be found all around, and in fact there are very few mechanical or electro-mechanical systems that do not include some kind of a feedback control device. In robotics, control design algorithms are responsible for the motion of the manipulators. In flight applications, control algorithms are designed for stabilization, altitude regulation and disturbance rejection. Cruise control is an interesting application in which the automobile's speed is set at a fixed value. In electronic amplifiers feedback is used to reduce the damaging influence of external noise. In addition, these days control systems can be found in diverse fields ranging from semiconductor manufacturing to environmental regulation.

This course is intended to present you with the basic principles and techniques for the design of feedback control systems. At this point in your study you have mastered the prerequisite topics such as dynamics and the basic mathematical tools that are needed for their analysis. Control system design relies on your knowledge in these fields but also requires additional skills in system interfacing. As you will see from this course, from further electives, or from future experience, the design of feedback control systems depends on

1. Knowledge of basic engineering principles such as dynamics, fluid mechanics, thermal science, electrical and electronic circuits, and materials. These tools are imoprtant, as we will soon see, for designing mathematical models of systems. In addition, thorough understanding of the underlying physics is very valuable in determining the most suitable control algorithms and hardware.
2. Knowledge of mathematical tools. In control system design, extensive use is made of matrices and differential equations, and therefore, you should be very comfortable with such concepts. Laplace transforms and complex variables are also used in control applications.
3. Knowledge of simulation techniques. System simulation is essential for verifying the accuracy of the model and for verifying that the final control design meets the desired specifications. In this course we will use the software Matlab to perform control design simulations.
4. Knowledge of contol design methodologies, and the basic capabilities and limitations of each control methodology. This aspect of the control design procedure will be the main goal of this course.
5. Knowledge of control hardware such as the different commercially available sensors and actuators. We will cover this part briefly in this course.
6. Knowledge of control software for data acquisition and for the implementation of control algorithms.

   Before we go on discussing the technical aspects of feedback control, we will give a very short outline of its historical beginnings. The use of feedback mechanisms can be traced back to devices that were invented by the Greeks such as liquid level control mechanisms. Early work on the mathematical aspects of feedback and control was initiated by the physicist Maxwell who developed a technique for determining whether or not systems which are governed by linear differential equations are stable. Other prominent mathematicians and physicists, such as Routh and Lyapunov, contributed greatly to the study of stability theory. Their results now form much of the backbone for control design.

   
   Historical Mechanism for Water Level Control.
   Click here to see the animation
   Click here to see an animation of a similar system

   The study of electronic feedback amplifiers provided the impetus for much of the progress of control design during the first part of the 20th century. The work of Nyquist (1932) and Bode (1945) used mathematical methods based on complex analysis for the analysis of the stability and performance of electronic amplifiers. These techniques are still in use in many technological applications as we will see in this course. Such complex analytic methods are currently called classical control techniques.

   During the second world war, advances in control design centered around the use of stochastic analysis techniques to model noise and the development of new methods for filtering and estimation. The MIT mathematician N. Wiener was very influential in this development. Also during that period, research at MIT Radiation Laboratory gave rise to more systematic design methods for servomechanisms.

   During the 1950's a different approach to the analysis and design of control systems was developed. This approach concentrated on differential equations and dynamical systems as opposed to complex analytic methods. One advantage of this approach is that it is intimately related to, physical modeling and can be viewed as a continuation to the methods of analytical mechanics. In addition, it provided a computationally attractive methodology for both analysis and design of control systems. Work by Kalman in the USA and Pontryagin in the USSR laid the foundation to what is currently called modern control.

   Recently, research aiming at providing reliable and robust control design algorithms resulted in a combination of complex analytic methods and dynamical systems methods. These recent approaches utilize the best features of each method. In this course we will develop techniques that are based on each one of these approaches. At that point it will become clearer what the relative merits are of these two approaches.